微扰法在静电电子透镜容差计算中的适用性分析

The Tolerance of Perturbation Method for Calculating of Electrostatic Lenses

对微扰法在电子光学系统容差计算中的适用性进行了分析．针对电极偏心和电极加工不圆这两种常见缺陷，研究了２个解析模型———偏心双圆筒电容器和共焦椭圆柱电极，推导了其电位分布的表达式．并用所编写的基于微扰法的计算软件，计算了相应的缺陷电极结构的电场分布．将数值计算结果与解析解对比，得到了微扰法的计算误差关于电极缺陷与尺寸比的变化曲线．结果表明，形位公差为１～３级时，微扰法的计算误差仅为１０－４。

The perturbation method is studied for calculating the tolerance of elecron optical systems. Analytical solutions are given for a cylindrical condenser with misalignment and a pair of confocal elliptic electrodes. The corresponding fields for defective electrode structures were calculated. The calculated error and the ratio of defect to dimension of electrodes were obtained. The relative errors are only about 10 -4 for defects with grades of 1～3. This is important the development to electron optical systems.